Question

Complete solution set of ${\tan }^2\left({\sin }^{-1}x\right)>1$ is

• A. $\left(-1,-\frac{1}{\sqrt{2}}\right)\cup \left(\frac{1}{\sqrt{2}},1\right)$
• B. $\left(-\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}\right)\sim \{0\}$
• C. $(-1,1)\sim \{0\}$
• D. None of these

Answer 1

Answer: (A)

${\tan }^2\left({\sin }^{-1}x\right)>1$
$\Rightarrow \frac{\pi }{4}<{\sin }^{-1}x<\frac{\pi }{2}$ or $-\frac{\pi }{2}<{\sin }^{-1}x<-\frac{\pi }{4}$
$\Rightarrow x\in \left(\frac{1}{\sqrt{2}},1\right)$ or $x\in \left(-1,-\frac{1}{\sqrt{2}}\right)$
$\Rightarrow x\in \left(-1,-\frac{1}{\sqrt{2}}\right)\cup \left(\frac{1}{\sqrt{2}},1\right)$